In the wake of the huge data breach, Target offered customers free credit monitoring.
However, Consumer Reports criticized the offer saying it gives consumer a false sense of security.
Target offered what it called "peace of mind" against the threat of thieves using stolen data to open new accounts in victims' names. The retailer offered free credit monitoring from Experian.
Consumer Reports called the offer better than nothing, but weak because it's only with Experian, and not the other two credit bureaus, Transunion and Equifax. The three credit bureaus can collect different information.
"Unless you're checking all three of them, you can miss someone trying to steal your identity and open new credit," said Consumer Reports' Margot Gilman.
To protect yourself, Gilman suggested consumer consider having the credit bureaus place a security freeze on their file.
"A security freeze is one of the best protections," Gilman said. "It blocks access to your credit information and makes it more difficult for a crook to open a new account under your name."
Small fees are involved in placing freezes and "thaws" when the consumer needs to lift the freeze when applying for new credit.
As for unauthorized charges on credit or debit cards, it's up the consumer to keep watch.